A sports writer wished to see if a football filled with helium travels farther, on average, than a football filled with air. To test this, the writer used 18 adult male volunteers. These volunteers were randomly divided into two groups of nine subjects each. Group 1 kicked a football filled with helium to the recommended pressure. Group 2 kicked a football filled with air to the recommended pressure. The mean distance for group 1 was 30 metres, with a standard deviation s_1 = 8 metres. The mean distance for group 2 was 26 metres, with a standard deviation s_2 = 6 metres. Assume the two groups of kicks are independent. Let \mu_1 and \mu_2 represent the mean distance we would observe for the entire population represented by the volunteers if all members of this population kicked, respectively, a helium- and an air-filled football. Assume that two-sample t-procedures are safe to use.
Suppose the researcher had wished to test the hypotheses

with a two-sample t-test (use the conservative method for the degrees of freedom). Which of the following conclusions is reasonable?

Question

A sports writer wished to see if a football filled with helium travels farther, on average, than a football filled with air. To test this, the writer used 18 adult male volunteers. These volunteers were randomly divided into two groups of nine subjects each. Group 1 kicked a football filled with helium to the recommended pressure. Group 2 kicked a football filled with air to the recommended pressure. The mean distance for group 1 was 30 metres, with a standard deviation   s_1  = 8 metres. The mean distance for group 2 was 26 metres, with a standard deviation   s_2  = 6 metres. Assume the two groups of kicks are independent. Let   \mu_1  and   \mu_2  represent the mean distance we would observe for the entire population represented by the volunteers if all members of this population kicked, respectively, a helium- and an air-filled football. Assume that two-sample t-procedures are safe to use. 
 Suppose the researcher had wished to test the hypotheses

with a two-sample t-test (use the conservative method for the degrees of freedom).  Which of the following conclusions is reasonable?

Answer

There is strong evidence (P > 0.10) that, on average, footballs filled with helium travel farther than footballs filled with air when kicked.

Answer

There is little evidence (P > 0.10) that, on average, footballs filled with helium travel farther than footballs filled with air when kicked.

Answer

There is little evidence (P < 0.05) that, on average, footballs filled with helium travel farther than footballs filled with air when kicked.

Answer

There is strong evidence (P < 0.05) that, on average, footballs filled with helium travel farther than footballs filled with air when kicked.

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A sports writer wished to see if a football filled with helium travels farther,...

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